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Solving Equations by by Solving Equations 1-2 1-2 Adding or Subtracting Adding or Subtracting Warm Up Lesson Presentation Holt McDougal Algebra 1 Algebra 1 Solving Equations by 1-2 Adding or Subtracting Warm Up Evaluate. 1. 2 + 4 1 3 3 2. 0.51 + (0.29) Evaluate each expression for a = 3 and b = 2. 3. a + 5 Holt McDougal Algebra 1 4. 12 b Solving Equations by 1-2 Adding or Subtracting Objective Solve one-step equations in one variable by using addition or subtraction. Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Vocabulary equation solution of an equation Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true. To find solutions, isolate the variable. What does Isolate mean? Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Isolate a variable by using inverse operations which "undo" operations on the variable. An equation is like a balanced scale. To keep the balance, perform the same operation on both sides. Inverse Operations Operation Inverse Operation Addition Subtraction Subtraction Holt McDougal Algebra 1 Addition Solving Equations by 1-2 Adding or Subtracting Properties of Equality WORDS Addition Property of Equality You can add the same number to both sides of an equation, and the statement will still be true. NUMBERS ALGEBRA Holt McDougal Algebra 1 3=3 3+2=3+2 5=5 a=b a+c=b+c Solving Equations by 1-2 Adding or Subtracting Properties of Equality WORDS Subtraction Property of Equality You can subtract the same number from both sides of an equation, and the statement will still be true. NUMBERS ALGEBRA Holt McDougal Algebra 1 7=7 7–5=7–5 2=2 a=b a–c=b–c Solving Equations by 1-2 Adding or Subtracting Example 1A: Solving Equations by Using Addition Solve the equation. Check your answer. y – 8 = 24 +8 +8 y = 32 Check Since 8 is subtracted from y, add 8 to both sides to undo the subtraction. y – 8 = 24 32 – 8 24 24 24 Holt McDougal Algebra 1 To check your solution, substitute 32 for y in the original equation. Solving Equations by 1-2 Adding or Subtracting Example 1B: Solving Equations by Using Addition Solve the equation. Check your answer. 5 =z– 7 7 7 Since is subtracted from z, add to 16 16 16 16 both sides to undo the subtraction. + 7 + 7 16 16 3=z 4 5 =z– 7 16 16 Check To check your solution, 5 3 – 7 3 substitute for z in the 4 16 16 4 original equation. 5 5 16 16 Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 1a Solve the equation. Check your answer. n – 3.2 = 5.6 + 3.2 + 3.2 n = 8.8 Check Since 3.2 is subtracted from n, add 3.2 to both sides to undo the subtraction. n – 3.2 = 5.6 8.8 – 3.2 5.6 5.6 5.6 Holt McDougal Algebra 1 To check your solution, substitute 8.8 for n in the original equation. Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 1b Solve the equation. Check your answer. –6 = k – 6 +6 + 6 Since 6 is subtracted from k, add 6 to both sides to undo the subtraction. 0=k Check –6 = k – 6 –6 0 – 6 –6 –6 Holt McDougal Algebra 1 To check your solution, substitute 0 for k in the original equation. Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 1c Solve the equation. Check your answer. 16 = m – 9 +9 + 9 Since 9 is subtracted from m, add 9 to both sides to undo the subtraction. 25 = m Check 16 = m – 9 16 25 – 9 16 16 Holt McDougal Algebra 1 To check your solution, substitute 25 for m in the original equation. Solving Equations by 1-2 Adding or Subtracting Example 2A: Solving Equations by Using Subtraction Solve the equation. Check your answer. m + 17 = 33 – 17 –17 Since 17 is added to m, subtract 17 m = 16 from both sides to undo the addition. Check m + 17 = 33 16 + 17 33 33 33 Holt McDougal Algebra 1 To check your solution, substitute 16 for m in the original equation. Solving Equations by 1-2 Adding or Subtracting Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Example 2B: Solving Equations by Using Subtraction Solve the equation. Check your answer. 4.2 = t + 1.8 –1.8 – 1.8 2.4 = t Check Since 1.8 is added to t, subtract 1.8 from both sides to undo the addition. To check your solution, 4.2 = t + 1.8 4.2 2.4 + 1.8 substitute 2.4 for t in the original equation. 4.2 4.2 Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 2a Solve the equation. Check your answer. d+ 1 =1 2 – 1 – 1 2 2 d= 1 Since 1 is added to d, subtract 1 from 2 2 both sides to undo the addition. 2 Check d+ 1 =1 2 1 + 1 2 2 1 Holt McDougal Algebra 1 1 1 To check your solution, substitute 1 for d in the 2 original equation. Solving Equations by 1-2 Adding or Subtracting Write an equation to represent each relationship. Then solve the equation. Ten Less than a number is equal to 12. A number decreased by 13 is equal to 7. Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 2c Solve the equation. Check your answer. 6 + t = 14 –6 –6 t= 8 Check Holt McDougal Algebra 1 Since 6 is added to t, subtract 6 from both sides to undo the addition. 6 + t = 14 6+8 14 14 14 To check your solution, substitute 8 for t in the original equation. Solving Equations by 1-2 Adding or Subtracting Example 3: Solving Equations by Adding the Opposite 2 . Solve – 5 + p = – 11 11 + 5 + 5 11 11 3 p= 11 Check Since – 5 is added to p, add 5 11 11 to both sides. – 5 +p=– 2 11 11 5 3 – 2 – + 11 11 11 2 2 – – 11 11 Holt McDougal Algebra 1 To check your solution, substitute 3 for p in the 11 original equation. Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 3b 5 . Check your answer. Solve – 3 + z = 4 4 3 +z= 5 – 4 4 Since – 3 is added to z, add 3 3 3 + 4 + 4 4 4 to both sides. z=2 Check To check your solution, – 3 +z= 5 4 4 substitute 2 for z in the 3 5 original equation. – +2 4 4 5 5 4 4 Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting Example 4: Application Over 20 years, the population of a town decreased by 275 people to a population of 850. Write and solve an equation to find the original population. decrease current original in minus is population population population p – d = c p – 275 =850 Substitute 275 for d and 850 for c. p – 275 = 850 + 275 + 275 p =1125 Since 275 is subtracted from p, add 275 to both sides to undo the subtraction. Holt McDougal Algebra 1 The original population was 1125 people. Solving Equations by 1-2 Adding or Subtracting Check It Out! Example 4 A person's maximum heart rate is the highest rate, in beats per minute, that the person's heart should reach. One method to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using this method, write and solve an equation to find a person's age if the person's maximum heart rate is 185 beats per minute. Holt McDougal Algebra 1 Solving Equations by 1-2 Adding or Subtracting North Carolina entered the Union x years after Pennsylvania. Write an expression that shows the year North Carolina entered the Union? The expression f 26 represents the year Alabama entered the Union, where f is the year Florida entered. In which year did Alabama enter the Union? The number of states that entered the Union in 1889 was half the number of states s that entered in 1788. Write an expression that shows the number of states that entered the Union in 1889? Holt McDougal Algebra 1